Label this plum tree graph to make it totally magic!
Find all the ways of placing the numbers 1 to 9 on a W shape, with
3 numbers on each leg, so that each set of 3 numbers has the same
A 2-Digit number is squared. When this 2-digit number is reversed
and squared, the difference between the squares is also a square.
What is the 2-digit number?
This problem involves making a connection between the pattern in
a sequence of numbers and the algebra that expresses the general
You can right-click and save to get your own copy of each
Number Patterns 1 and Interactive
Number Patterns 2
Open the spreadsheet called Interactive Number Patterns 1 and
experiment with the control buttons. You should discover that the
red and blue numbers in the boxes, and also the algebra, can be
made to show or not show. You should also discover that the numbers
and the algebra can be changed.
Adjust the view size if necessary using Zoom on the View
Challenge One has three
Hide the blue numbers in the boxes, change the algebra and the
red numbers and check you can successfully predict the hidden blue
Next hide the red numbers instead and repeat the challenge.
Explain to a friend how you manage this. You could even work in
pairs to set challenges for each other.
Finally hide the algebra. Change it without showing it, then
predict the formula. You have succeeded with this task when you can
explain your method to someone else.
Predict the hidden blue
Predict the hidden red, explaining your method
Predict the hidden algebra, again explaining your method and
especially why it works
And the "solutions" we would love to receive from you are your
best ways of justifying this important method.
Even when we cannot immediately explain why a method is valid it
is good to keep it in mind as something we very much want to